What is the the portfolio equity of a log short strategy? Is it used as denominator to compute rate of return for the long short strategy. Thanks.

please rephrase this attempt at a question.

In other words, is size of portfolio equity equal to the value of the cash position resulting from shorting securities?

as far as I understood - you have a portfolio. you are using long/short to do active management. and there is a zero balance position (which is market neutral).

Your portfolio equity is not affected by this transaction. You gain alpha because of your insights on the long and short - long is purchased undervalued - if it goes up - you get an alpha. Short was overvalued - you gain alpha because it went down further. – since it is same industry, equal amounts invested in long and short - you have no beta, only alpha from this.

you got some cash because you shorted the position - which you earn interest on.

your portfolio position + money received from the short - can be invested in a market index elsewhere to earn a market beta.

your borrowed amount - is the amount from the shorting.

your equity = original portfolio you had.

I think it is not used in denominator to compute rate of return since this value could be zero i.e. position in derivatives require almost zero or minimal margin investment.

I think mostly Hedge fund apply this strategy. For performance appraisal, absolute return above some hurdle rate should be used.

OR

Rate of return = (ending value - begining value) / beg value. Deleveraging of the begining value should be done.